After Key Squares in pawn endgames, the next fundamental concept in King and pawn endgames is opposition.
What is the opposition
If you have the opposition, your opponent will be forced to leave this spot first, and you can use this to reach important squares with your King.
We can therefore see the opposition as a particular case of Zugzwang, where each side would prefer to pass rather than playing a move. Now, coming back to Key Squares in King and pawn endgame, you can use the opposition to try to bring your King on those key squares.
The opposition in basic pawn endgames
This example is particularly interesting as it reminds us that opposition is only a mean to help you reaching important squares. But if you can do so without taking the opposition, then do it !
A more complex example
The move Ke7 by Black is an example of what we call Distant Opposition, which is a generalization of the concept of opposition.
A really beautiful example and an illustration of how subtle Pawn endings can be !
But it goes further than that ! We can also consider cases where the Kings are not facing each other !
Thus, diagonal and distant opposition are distinct flavors of the same very important concept of opposition.
The final position is winning for White. All you need to know how is to win with a remote passed pawn, an article that will soon be online.
This was an example of “distant opposition in real life” where knowing about the distant opposition concept helped you find a move that you would else have struggled to justify.
Once again, I must emphasize that opposition is a mean to reach some important squares and not an end in itself. It is however an absolute must in pawn endgames and a very powerful mean to win king and pawn endgames with the opposition.